Locomotory Advantages to Flapping Out of Phase

The interactions between two fish swimming side by side are examined. An inviscid fluid model is employed to argue that flapping out of phase can lead to locomotory advantages for both fish. Two effects are examined: (a) the effect of the cooperation between the wakes of the two fish in increasing their forward swimming velocities and (b) the effect of the coupling between the lateral oscillations of the fish and the circulations around their bodies in enhancing their forward swimming motion. The models are stripped to their simplest level in order to highlight these effects.